Analyzing mixibility of well cement slurries

ABSTRACT

Some aspects of what is described here relate to analyzing a well cement slurry. In some aspects, a well cement slurry is mixed in a mixer under a plurality of conditions. The plurality of conditions correspond to a plurality of distinct Reynolds number values for the well cement slurry in the mixer. Power number values associated with mixing the well cement slurry in the mixer under the plurality of conditions are identified. Each power number value is based on an amount of energy used to mix the well cement slurry under a respective one of the plurality of conditions. Values for parameters of a functional relationship between power number and Reynolds number are identified based on the power number values and the Reynolds number values for the plurality of conditions.

CROSS-REFERENCE TO RELATED APPLICATION

This application is the National Stage of, and therefore claims thebenefit of, International Application No. PCT/US2014/053245 filed onAug. 28, 2014, entitled “ANALYZING MIXABILITY OF WELL CEMENT SLURRIES,”which was published in English under International Publication Number WO2016/032498 on Mar. 3, 2016. The above application is commonly assignedwith this National Stage application and is incorporated herein byreference in its entirety.

BACKGROUND

The following description relates to analyzing mixability of well systemfluids, including well cement slurries and other types of well systemfluids.

Cement compositions may be used in a variety of subterranean operations,such as, in the production and exploration of hydrocarbons, e.g., oil,gas, and other hydrocarbons, onshore and offshore. For example, asubterranean well can be constructed using a pipe string (e.g., casing,liners, expandable tubulars, etc.), which can be run into a wellbore andcemented in place. The process of cementing the pipe string in place iscommonly referred to as “primary cementing.” In a typical primarycementing method, a cement composition is pumped into an annulus betweenthe wellbore and the exterior surface of the pipe string disposedtherein. The cement composition can set in the annular space, therebyforming an annular sheath of hardened, substantially impermeable cement(i.e., a cement sheath). The cement sheath can support and position thepipe string in the wellbore and bond the exterior surface of the pipestring to the subterranean formation. The cement sheath surrounding thepipe string functions to prevent the migration of fluids in the annulusamong other things, and to protect the pipe string from corrosion.

A broad variety of well cement compositions have been used insubterranean well cementing operations. Such well cement compositionscan be made, for example, by mixing portland cement with water and oftenwith one or more other additives such as retarders, accelerators, andlightweight additives. The additives can be either dry powder, liquid orboth. The components are mixed under certain mixing conditions (e.g.,mixing speeds, mixing times, and other conditions). For example,industry guideline specifications for laboratory experiments designed tomimic field operations, which include quantities and mixing conditions,for mixing a specified volume of a cement composition are provided,e.g., by institutions such as the American Petroleum Institute (API) orother institutions.

DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of example systems for mixing a wellcement slurry.

FIG. 2 is flow chart showing an example process for analyzing mixabilityof well cement slurries.

FIG. 3 is a schematic diagram of an example data analysis system.

FIG. 4 illustrates a system for preparation and delivery of a cementcomposition to a wellbore.

FIG. 5A illustrates surface equipment that may be used in placement of acement composition in a wellbore.

FIG. 5B illustrates placement of a cement composition into a wellboreannulus.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

In some implementations of what is described here, an algorithm is usedto determine the mechanical energy to mix a well system fluid, forexample, at the lab scale or in the field. With knowledge of the energyrequirements, a comparison of the predicted energy requirements withpreviously-mixed “easy to mix” and “hard to mix” slurries can be made,and a slurry can hence be classified according to an objective orquantitative “mixability index.” In some instances, the algorithm savestime, labor and money when dealing with difficult to mix slurries.

The American Petroleum Institute (API) recommends the industry guidelinestandard for mixing well cement slurries in the lab, and it recommendsspecifications for mixing a specific volume of neat well cement slurriesat certain speeds for certain periods of time. When additives areincorporated into the well cement slurry, and also when larger volumesare mixed, maintaining these mixing parameters becomes difficult andthis results in different levels of energy input/consumption.Furthermore, field equipment capabilities differ from laboratory-basedequipment, and consequently, well cement slurries may be mixable in thelaboratory (e.g., under API mixing specifications) but fail to mix orbecome very difficult to mix in the field.

In some aspects of what is described here, a predictive algorithm isused to determine the energy consumption requirements for mixing of wellcement slurries in the laboratory. In some implementations, the energyconsumption during the process of laboratory mixing of well cementslurries is measured directly, for example, as described inInternational Application PCT/US2013/067874, filed on Oct. 31, 2013,entitled, “Correlating Energy to Mix Cement Slurry Under DifferentMixing Conditions.” The predictive algorithm may then be used to make apriori predictions of the energy consumption of a previously-known or apreviously-unknown cement slurry. Such an algorithm can help quantifythe “mixability” of a well cement slurry based on the energy consumptionand save much time and labor in designing well cement slurries for jobs,thereby potentially helping alleviate costs associated with mixingissues in the field.

FIG. 1 is a schematic diagram of two example systems for mixing a wellcement slurry. The two example systems are a laboratory system 100 and afield system 120. The laboratory system 100 includes a laboratory mixer102 in a laboratory environment where well cement slurries can betested. The field system 120 includes a field mixer 122 where wellcement slurries are prepared for use in a well site 124. The field mixer122 can be of a different configuration than the laboratory mixer 102.For example, the laboratory mixer 102 can be an electric mixer, and thefield mixer 122 can be a hydraulic mixer, a static mixer, an agitatorsystem or other mixer that is different from the laboratory mixer 102.

Some example field mixers include a mixing vessel having a diameter inthe range of approximately 24-inches to 36-inches, and operate at anagitation speed of approximately zero to 2,000 rotations per minute(RPM). Some example laboratory mixers include a mixing vessel having adiameter in the range of approximately 6-inches, and operate at anagitation speed of approximately zero to 12,000 rotations per minute(RPM). Other types of mixers can be used to mix a well cement slurry ina laboratory environment, in a field environment, or in anotherenvironment (e.g., a Hobart mixer, etc.).

The laboratory mixer 102 can be configured to mix a well cement slurry,for example, under API specifications or other specifications. Thelaboratory mixer 102 can be an electric mixer that includes, e.g., animpeller 104 connected to a motor 106 to rotate the impeller 104. Thelaboratory mixer 102 can be connected to a measurement device 108 todirectly measure electrical power supplied to the mixer in mixing aspecified well cement slurry. In some implementations, the measurementdevice 108 can be a multimeter connected to the motor 106 to measureparameters to determine the electrical power, e.g., a voltage across themotor 106, a current through the motor 106, other parameters orcombinations of them. The laboratory system 100 can also includeadditional measurement devices, for example, to measure the properties(e.g., mass, density, viscosity, etc.) of the well cement slurry in themixer.

The measurement device 108 can be connected to a computer system 110which includes one or more processors 112 and a computer-readable medium114 storing instructions executable by the one or more processors 112 toanalyze data from mixing of the well cement slurry. The computer system110 can include a computer, e.g., a desktop computer, a laptop computer,a smartphone, a tablet computer, a personal digital assistant (PDA) orother computer. The computer system 110 can be connected to one or moreinput devices 116 and one or more output devices 118. In someimplementations, the computer system 110 can be implemented as hardwareor firmware integrated into the measurement device 108. Alternatively,or in addition, the measurement device 108 can be integrated into thecomputer system 110. In some implementations, data from the measurementdevice 108 can be manually input into the computer system 110, e.g.,using the one or more input devices 116.

Sometimes well cement slurries mix with ease in the laboratory, but posechallenges when mixed using field equipment. Some of the major reasonsfor the discrepancy between the laboratory and the field mixes mayinclude, but are not limited to (a) inadequate comprehension of powerrequirements for mixing of well cement slurries in the laboratory, and(b) inaccurate power consumption requirement for mixing well cementslurries under field conditions, as correlated to the power consumptionrequirements in the laboratory. Existing API mixing specificationsfollowed in the laboratory are unable to help evaluate anorder-of-magnitude power consumption requirement of the mixing ofcomplex slurries in the field versus in the laboratory or to helpevaluate the “mixability” of well cement slurries in the field vis-à-visin the laboratory.

Some implementations of the techniques described here can predict powerconsumption requirements for mixing of a fluid (e.g., well cementslurries and other well system fluids), before actual measurement of thefluid, knowing identified design variables. Then, knowing the powerconsumption requirements for mixing of previously “easy-to-mix” wellcement slurries and “hard-to-mix” well cement slurries, an unknownslurry can be classified as “mixable” or not, based on powerconsumptions for mixing it in the laboratory. A theoreticalconsideration for the algorithm is included in the following discussionof the predictive algorithms and related techniques.

Power consumption in a batch mixer can be estimated from the followingequation:

$\begin{matrix}{\frac{P}{V} = {\tau_{average} \times {\gamma_{average}.}}} & {{Eqn}\mspace{14mu}(1)}\end{matrix}$

Further equations relating to mixing in a batch mixer are as follows:

$\begin{matrix}{{N_{P} = \frac{\int{\frac{P}{{\rho(t)}N^{3}D^{5}}{dt}}}{\int{dt}}},} & {{Eqn}\mspace{14mu}(2)} \\{{Re} = {\frac{\int{\frac{\rho\;{ND}^{2}}{\mu(t)}{dt}}}{\int{dt}}.}} & {{Eqn}\mspace{14mu}(3)}\end{matrix}$

In the equations above, the following variables are used:

τ_(average)=Average Shear Stress in the fluid in the batch mixer (Pa);

γ_(average)=Average Shear Rate in the fluid in the batch mixer (s⁻¹);

P=Power consumed in the batch mixer because of impeller motion (Watt);

N_(p)=Time-average Power Number for the particular impeller used in thelaboratory blender/field mixer (dimensionless), following the temporalevolution of density when mixing dry cement blend with mix water.Spatial variations can be accounted for as well, if so deemed necessary;ρ=Homogenous density of the fluid in the batch mixer (kg m⁻³). Thiswould be time-varying, until complete homogeneity is attained (severalseconds). A method such as static/dynamic light scattering or othersuitable methods might be employed to follow the evolution of thisparameter with time;V=Volume of fluid (m³);N=Agitation speed (s⁻¹);D=Diameter of the impeller (m);μ=Apparent viscosity (also referred to as Plastic Viscosity or PV) ofnon-Newtonian fluid (Pa-s). This would be time-varying, until completehomogeneity is attained (several seconds). A method such asstatic/dynamic light scattering or other suitable methods might beemployed to follow the evolution of this parameter with time, along withusing appropriate methods to calculate the viscosities; andRe=Time-averaged Reynolds Number characterizing the fluid motion in thebatch mixer (dimensionless), following the temporal evolution ofviscosity when mixing dry cement blend with mix water. Spatialvariations can be accounted for as well, in some cases.

Scale-up considerations and power consumption in agitator systems can beanalyzed based on the Buckingham pi theorem formulation, considering adimensional analysis of the various factors that contribute to powerconsumption:

$\begin{matrix}{{f\left( {\frac{D^{2}N\;\rho}{\mu},\frac{{DN}^{2}}{g},\frac{P}{\rho\; N^{3}D^{5}},\frac{D}{T},\frac{D}{Z},{others}} \right)} = 0.} & {{Eqn}\mspace{14mu}(4)}\end{matrix}$

In the equation above, “others” refers to other groups of geometricsimilarity, and:

g=Universal constant (acceleration due to gravity) (m/s²);

T=Diameter of blender tank (m); and

Z=Ratio of tank diameter to impeller diameter (dimensionless).

Equation (4) above can also be re-written as:N _(p) =C(Re)^(x)(Fr)^(y)(others)  Eqn (5),where “others” refers to other dimensionless groups of geometricsimilarity, raised to their respective powers, and Fr refers to theFroude number (characteristic of vortex formation in stirred systems).

Keeping blender geometry and impeller geometry parameters constant(e.g., adhering to the standard WARING® blender recommended forlaboratory mixing by API), the above Equation (5) can be written as:N _(p) =C(Re)^(x)(Fr)^(y)  Eqn (6).

This can further be expressed as:ϕ=N _(p)/(Fr)^(y) =C(Re)^(x)  Eqn (7),where ϕ refers to the power function (characteristic of powerconsumption for stirring). The contribution of the Froude number (whichis relevant for the effects of vortexing and surface aeration in batchmixers) for this instance can be neglected, and y=0. Hence,ϕ=N _(p) =C(Re)^(x)  Eqn (8)

Hence, for the mixing of well cement slurries in the laboratory, thepower function is the power number for the particular stirred system inconsideration. This also indicates that the power number will be afunction of the variables that define the Reynolds number of the stirredsystem. Based on the equations above, an algorithm can be used forevaluating power consumption for laboratory mixing of well cementslurries and other well system fluids.

FIG. 2 is a flowchart of an example process 200 for analyzing mixabilityof well cement slurries. In some implementations, at least a portion ofthe process 200 can be implemented by the laboratory mixer 102, themeasurement device 108, the computer system 110 or combinations of them.In some implementations, at least a portion of the process 200 can beimplemented by the field mixer 122, measurement devices, an operator, orcombinations of them.

In some implementations, the process 200 can be scientifically morerigorous, more direct and more portable across laboratories or othersettings, for example, as compared to existing techniques (e.g.,conventional techniques that are based on the incorporation ofapproximation and the evaluation of certain constants of approximation).In some implementations, the process 200 provides a quantitativetechnique to evaluate the mixability of a well cement slurry in thefield based on laboratory data, and also an improved method in thescientific evaluation of well system fluid mixability and on therequired energy consumption.

Generally, the process 200 can be used with any type of mixer, in avariety of environments and with any type of well system fluid. In thefollowing discussion, an example of an electric mixer mixing well cementslurries in a lab environment is considered. The process 200 can be usedin the example application or in other applications to assign amixability index to a new well system fluid mixture. In some cases, themixability index can be computed for a variety of fluids to be mixed bythe same mixer.

Initially in the process 200, constituents of a well cement slurry arereceived. The constituents can include a quantity of each well cementslurry component to be mixed, a quantity of water (or other fluid) to beadded to mix the multiple components, etc.

At 202, the components of the specified well cement slurry are mixed ina mixer. To do so, respective quantities of components of the wellcement slurry (e.g., hydraulic cement, water, additives, or othercomponents) can be added to the mixer. In some implementations, dryadditives can also be added to the liquids in the well cement slurry. Inone example instance, the motor 106 can be operated to rotate theimpeller 104 at a specified speed of mixing and for a specified time ofmixing to mix the multiple components of the well cement slurry. Inother example instances, the motor 106 can be operated to rotate theimpeller 104 at respective (e.g., different or time-varying) speeds ofmixing and for respective (e.g., different) times of mixing to mix themultiple components of the well cement slurry.

Also at 202, the average power consumed by the mixer mixing the wellcement slurry is measured. The power used by the mixer in mixing thewell cement slurry can be measured, for example, as described inInternational Application PCT/US2013/067874, filed on Oct. 31, 2013,entitled, “Correlating Energy to Mix Cement Slurry Under DifferentMixing Conditions,” or the power can be measured in another manner. Insome examples, a voltage across and a current drawn by the mixer can bedirectly measured while mixing the well cement slurry. In someimplementations, a measurement device (e.g., a multimeter) can bedirectly connected to the motor of the mixer to measure the voltageacross and the current drawn by the motor while mixing. The measurementdevice can be implemented to obtain multiple measurements of voltage andcurrent, each measurement corresponding to a respective instance ofoperating the motor at a mixing speed for a mixing time.

In some implementations, the energy to mix the specified well cementslurry can be determined based on the measured voltage and the current.For instance, the measurement device can transmit the measured voltageand current to a data analysis system, which can implement computeroperations to determine the electrical power, e.g., as a product ofvoltage and current. For example, the voltage and current can bemeasured for a period of time in the laboratory system under thelaboratory conditions. The electrical power can be determined as aproduct of a time-averaged voltage and a time-averaged current. For themultiple instances of operating the motor, the data analysis system candetermine multiple values of electrical power, each value being aproduct of a respective time-averaged voltage and time-averaged current.Upon measuring the electrical power supplied to the mixer, the energy tomix the specified well cement slurry from the measuring can bedetermined. In some implementations, the energy can be electrical energydetermined as a product of electrical power and the time of applicationof the electrical power. In some examples, the average power consumed bya WARING® blender in the laboratory under a constant-held motorrotational speed (N) is measured.

In some cases, the well cement slurry is completely mixed andhomogeneous before measuring the energy consumed by the mixer. In somecases, the well cement slurry is unmixed and non-homogeneous when theenergy measurements commence.

At 204, the power number is calculated. For example, knowing thetemporal evolution of the density of the slurry design used, one cancalculate the power number N_(p) of this system under this condition,with the help of Equation (2) above. In some cases, the temporalevolution can be neglected.

At 206, the Reynolds number of the fluid in the mixer is calculated. Forexample, knowing the density and apparent viscosity of the fluid, thesize of the impeller and agitation speed of the mixer, and otherrelevant parameters, Equation (3) above can be used to compute theReynolds number.

At 208, the rotational speed (N) of the mixer impeller is varied and theoperations 202, 204, 206 are repeated for one or more distinctrotational speeds. For example, the rotational speed of the blendermotor can be varied to different (e.g., constantly-held, ortime-varying) rotational speeds to measure the power consumed by theblender. Thereupon, the variation of the power number N_(p) of thesystem with a blender RPM can be measured. Typically, this shouldgenerate a function of the form:N _(p) =f(N)  Eqn (9).

At 210, the density (ρ) of the well cement slurry is varied, and theoperations 202, 204, 206, 208 are repeated for one or more distinctdensities. Typically, this should generate a function of the form:N _(p) =f(N,ρ)  Eqn (10).

At 212, the apparent viscosity (μ) (also referred to as plasticviscosity or PV) of the well cement slurry is varied, and the operations202, 204, 206, 208, 210 are repeated for one or more distinct apparentviscosities. Typically, this should generate a function of the form:N _(p) =f(N,ρ,μ)  Eqn (11)

For each combination of the variables N, ρ, and μ, the associatedReynolds number Re is calculated at 206 utilizing Equation 3. This cangenerate a function of the form:N _(p) =f(Re)  Eqn (12)

A comparison of Eqns (8) and (12) show that the following may be graphedfor different values of N, ρ, and μ:N _(p) =C(Re)^(x)  Eqn (13).Eqn (13) provides of a functional relationship between power number(N_(p)) and Reynolds number (Re), and values for the parameters C and xcan be identified based on data points (e.g., the power number valuesand the Reynolds number values) from each iteration of the operationsshown in FIG. 2. For example, the data points can be fitted or otherwiseanalyzed to compute particular values for the parameters C and x. Insome cases, the data points are fitted using least-squares regression oranother type of fitting technique.

In some cases, the parameters C and x are constants. The variation ofthe parameters would not be expected to be large for a particular fluidsystem, e.g., well cement slurry systems. Hence, based on theparticulars of the speed of agitation, density and apparent viscosity ofthe slurry to be mixed, an operating value of the power number N_(p) maybe pre-evaluated based on the graphical form of Eqn (13) from previouslyconducted experiments. Then, based on the value of the power numberN_(p), and using Eqn (2), an operating value of the power required formixing the slurry contents at any pre-determined conditions of N, ρ, andμ may be evaluated, thereby giving an order-of-magnitude estimate of theenergy requirements for mixing of an unknown well cement slurry. Thischaracteristic will be useful, for example, when pre-determining the“mixability” of the well cement slurry through a comparison of thepredicted energy requirements with previously mixed “easy to mix” and“hard to mix” slurries, and in other contexts. This process can savetime, labor and money, for example, when dealing with difficult to mixslurries.

FIG. 3 is a schematic diagram of an example data analysis system 300that includes a computer system 302 and a display device 304. The dataanalysis system 300 can be located at a data-processing center, acomputing facility, or another location. The example data analysissystem 300 can communicate with (e.g., send data to or receive datafrom) a mixing system. For example, the data analysis system 300 mayreceive data from either of the example systems in FIG. 1 or anothertype of mixing system. In some examples, all or part of the dataanalysis system 300 may be included with or embedded in a mixing system.The data analysis system 300 or any of its components can be locatedwith or apart from a mixing system.

In some implementations, the data analysis system 300 can include or beimplemented on various types of devices, including, but not limited to,personal computer systems, desktop computer systems, laptops, mainframecomputer systems, handheld computer systems, application servers,computer clusters, distributed computing systems, workstations,notebooks, tablets, storage devices, or another type of computing systemor device.

The example display device 304 can produce a visual output. The displaydevice 304 can include a computer monitor (e.g., LCD screen), aprojector, a printer, a touchscreen device, a plotter, or a combinationof one or more of these. In some instances, the display device 304displays data obtained by a mixing system, plots of data obtained byanalyzing mixing data, or other types of information.

As shown in the schematic diagram in FIG. 3, the example computer system302 includes a memory 316, a processor 314, and input/output controllers312 communicably coupled by a bus 313. A computing system can includeadditional or different features, and the components can be arranged asshown or in another manner. The memory 316 can include, for example, arandom access memory (RAM), a storage device (e.g., a writable read-onlymemory (ROM) or others), a hard disk, or another type of storage medium.The computer system 302 can be preprogrammed or it can be programmed(and reprogrammed) by loading a program from another source (e.g., froma CD-ROM, from another computer device through a data network, or inanother manner).

In some examples, the input/output controllers 312 are coupled toinput/output devices (e.g., a monitor, a mouse, a keyboard, or otherinput/output devices) and to a network. The input/output devices cancommunicate data in analog or digital form over a serial link, awireless link (e.g., infrared, radio frequency, or others), a parallellink, or another type of link. The network can include any type ofcommunication channel, connector, data communication network, or otherlink. For example, the network can include a wireless or a wirednetwork, a Local Area Network (LAN), a Wide Area Network (WAN), aprivate network, a public network (such as the Internet), a WiFinetwork, a network that includes a satellite link, or another type ofdata communication network.

The memory 316 can store instructions (e.g., computer code) associatedwith an operating system, computer applications, and other resources.The memory 316 can also store application data and data objects that canbe interpreted by one or more applications or virtual machines runningon the computer system 302. As shown in FIG. 3, the example memory 316includes data 318 and applications 317. The data 318 can include wellcement slurry data, fluid data, mixer data, or other types of data. Theapplications 317 can include data analysis software, simulationsoftware, or other types of applications. In some implementations, amemory of a computing device includes additional or different data,application, models, or other information.

The processor 314 can execute instructions, for example, to generateoutput data based on data inputs. For example, the processor 314 can runthe applications 317 by executing or interpreting the software, scripts,programs, functions, executables, or other modules contained in theapplications 317. The input data received by the processor 314 or theoutput data generated by the processor 314 can include any of the mixingdata, cement slurry data, parameter data, or other information.

The example well cement slurries described above may directly orindirectly affect one or more components or pieces of equipmentassociated with the preparation, delivery, recapture, recycling, reuse,or disposal of the disclosed binder compositions. For example, the wellcement slurries may directly or indirectly affect one or more mixers,related mixing equipment, mud pits, storage facilities or units,composition separators, heat exchangers, sensors, gauges, pumps,compressors, and the like used to generate, store, monitor, regulate, orrecondition the well cement slurries. The well cement slurries may alsodirectly or indirectly affect any transport or delivery equipment usedto convey the binder compositions to a well site or downhole such as,for example, any transport vessels, conduits, pipelines, trucks,tubulars, or pipes used to compositionally move the well cement slurriesfrom one location to another, any pumps, compressors, or motors (e.g.,topside or downhole) used to drive the well cement slurries into motion,any valves or related joints used to regulate the pressure or flow rateof the well cement slurries, and any sensors (i.e., pressure andtemperature), gauges, or combinations thereof, and the like. The wellcement slurries may also directly or indirectly affect the variousdownhole equipment and tools that may come into contact with the cementcompositions/additives such as, for example, wellbore casing, wellboreliner, completion string, insert strings, drill string, coiled tubing,slickline, wireline, drill pipe, drill collars, mud motors, downholemotors or pumps, cement pumps, surface-mounted motors or pumps,centralizers, turbolizers, scratchers, floats (e.g., shoes, collars,valves, etc.), logging tools and related telemetry equipment, actuators(e.g., electromechanical devices, hydromechanical devices, etc.),sliding sleeves, production sleeves, plugs, screens, filters, flowcontrol devices (e.g., inflow control devices, autonomous inflow controldevices, outflow control devices, etc.), couplings (e.g.,electro-hydraulic wet connect, dry connect, inductive coupler, etc.),control lines (e.g., electrical, fiber optic, hydraulic, etc.),surveillance lines, drill bits and reamers, sensors or distributedsensors, downhole heat exchangers, valves and corresponding actuationdevices, tool seals, packers, cement plugs, bridge plugs, and otherwellbore isolation devices, or components, and the like.

Referring now to FIG. 4, a system that may be used in the preparation ofa cement composition will now be described. FIG. 4 illustrates a system2 for preparation of a cement composition and delivery to a wellbore. Asshown, the cement composition may be mixed in mixing equipment 4, suchas a jet mixer, re-circulating mixer, or a batch mixer, for example, andthen pumped via pumping equipment 6 to the wellbore. In some instances,the mixing equipment 4 and the pumping equipment 6 may be disposed onone or more cement trucks. In some instances, a jet mixer may be used,for example, to continuously mix the composition, including water, as itis being pumped to the wellbore.

An example technique and system for placing a cement composition into asubterranean formation will now be described with reference to FIGS. 5Aand 5B. FIG. 5A illustrates surface equipment 10 that may be used inplacement of a cement composition. While FIG. 5A generally depicts aland-based operation, the principles are applicable to subsea operationsthat employ floating or sea-based platforms and rigs. As illustrated byFIG. 5A, the surface equipment 10 may include a cementing unit 12, whichmay include one or more cement trucks. The cementing unit 12 may includemixing equipment 4 and pumping equipment 6 (e.g., FIG. 4). The cementingunit 12 may pump a cement composition 14 through a feed pipe 16 and to acementing head 18 which conveys the cement composition 14 downhole.

Turning now to FIG. 5B, the cement composition 14 may be placed into asubterranean formation 20. As illustrated, a wellbore 22 may be drilledinto the subterranean formation 20. While wellbore 22 is shown extendinggenerally vertically into the subterranean formation 20, wellbores mayextend at an angle through the subterranean formation 20, such ashorizontal and slanted wellbores. As illustrated, the wellbore 22comprises walls 24. In the example shown, a surface casing 26 has beeninserted into the wellbore 22. The surface casing 26 may be cemented tothe walls 24 of the wellbore 22 by cement sheath 28. One or moreadditional conduits (e.g., intermediate casing, production casing,liners, etc.) shown here as casing 30 may also be disposed in thewellbore 22. As illustrated, there is a wellbore annulus 32 formedbetween the casing 30 and the walls 24 of the wellbore 22 or the surfacecasing 26. One or more centralizers 34 may be attached to the casing 30,for example, to centralize the casing 30 in the wellbore 22 prior to andduring the cementing operation.

With continued reference to FIG. 5B, the cement composition 14 may bepumped down the interior of the casing 30. The cement composition 14 maybe allowed to flow down the interior of the casing 30 through the casingshoe 42 at the bottom of the casing 30 and up around the casing 30 intothe wellbore annulus 32. The cement composition 14 may be allowed to setin the wellbore annulus 32, for example, to form a cement sheath thatsupports and positions the casing 30 in the wellbore 22. Othertechniques may also be utilized for introduction of the cementcomposition 14. By way of example, reverse circulation techniques may beused that include introducing the cement composition 14 into thesubterranean formation 20 by way of the wellbore annulus 32 instead ofthrough the casing 30.

As it is introduced, the cement composition 14 may displace other fluids36, such as drilling fluids or spacer fluids, that may be present in theinterior of the casing 30 or the wellbore annulus 32. At least a portionof the displaced fluids 36 may exit the wellbore annulus 32 via a flowline 38 and be deposited, for example, in one or more retention pits 40(e.g., a mud pit), as shown on FIG. 5A. Referring again to FIG. 5B, abottom plug 44 may be introduced into the wellbore 22 ahead of thecement composition 14, for example, to separate the cement composition14 from the fluids 36 that may be inside the casing 30 prior tocementing. After the bottom plug 44 reaches the landing collar 46, adiaphragm or other suitable device ruptures to allow the cementcomposition 14 through the bottom plug 44. In FIG. 5B, the bottom plug44 is shown on the landing collar 46. In the illustrated example, a topplug 48 may be introduced into the wellbore 22 behind the cementcomposition 14. The top plug 48 may separate the cement composition 14from a displacement fluid 50 and also push the cement composition 14through the bottom plug 44.

Some of the subject matter and operations described in thisspecification can be implemented in digital electronic circuitry, or incomputer software, firmware, or hardware, including the structuresdisclosed in this specification and their structural equivalents, or incombinations of one or more of them. Some of the subject matterdescribed in this specification can be implemented as one or morecomputer programs, i.e., one or more modules of computer programinstructions, encoded on a computer storage medium for execution by, orto control the operation of, data-processing apparatus. A computerstorage medium can be, or can be included in, a computer-readablestorage device, a computer-readable storage substrate, a random orserial access memory array or device, or a combination of one or more ofthem. Moreover, while a computer storage medium is not a propagatedsignal, a computer storage medium can be a source or destination ofcomputer program instructions encoded in an artificially generatedpropagated signal. The computer storage medium can also be, or beincluded in, one or more separate physical components or media (e.g.,multiple CDs, disks, or other storage devices).

The term “data-processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, a system on a chip, or multipleones, or combinations, of the foregoing. The apparatus can includespecial purpose logic circuitry, e.g., an FPGA (field programmable gatearray) or an ASIC (application specific integrated circuit). Theapparatus can also include, in addition to hardware, code that createsan execution environment for the computer program in question, e.g.,code that constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, a cross-platform runtimeenvironment, a virtual machine, or a combination of one or more of them.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages. A computer program may, but need not, correspondto a file in a file system. A program can be stored in a portion of afile that holds other programs or data (e.g., one or more scripts storedin a markup language document), in a single file dedicated to theprogram, or in multiple coordinated files (e.g., files that store one ormore modules, sub programs, or portions of code). A computer program canbe deployed to be executed on one computer or on multiple computers thatare located at one site or distributed across multiple sites andinterconnected by a communication network.

Some of the processes and logic flows described in this specificationcan be performed by one or more programmable processors executing one ormore computer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andprocessors of any kind of digital computer. Generally, a processor willreceive instructions and data from a read-only memory or a random-accessmemory or both. A computer can include a processor that performs actionsin accordance with instructions, and one or more memory devices thatstore the instructions and data. A computer may also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic disks,magneto optical disks, or optical disks. However, a computer need nothave such devices. Devices suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices (e.g., EPROM, EEPROM, flash memory devices, and others),magnetic disks (e.g., internal hard disks, removable disks, and others),magneto optical disks, and CD ROM and DVD-ROM disks. In some cases, theprocessor and the memory can be supplemented by, or incorporated in,special purpose logic circuitry.

To provide for interaction with a user, operations can be implemented ona computer having a display device (e.g., a monitor, or another type ofdisplay device) for displaying information to the user and a keyboardand a pointing device (e.g., a mouse, a trackball, a tablet, a touchsensitive screen, or another type of pointing device) by which the usercan provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well; for example, feedbackprovided to the user can be any form of sensory feedback, e.g., visualfeedback, auditory feedback, or tactile feedback; and input from theuser can be received in any form, including acoustic, speech, or tactileinput. In addition, a computer can interact with a user by sendingdocuments to and receiving documents from a device that is used by theuser; for example, by sending web pages to a web browser on a user'sclient device in response to requests received from the web browser.

A computer system may include a single computing device, or multiplecomputers that operate in proximity or generally remote from each otherand typically interact through a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), an inter-network (e.g., the Internet), a networkcomprising a satellite link, and peer-to-peer networks (e.g., ad hocpeer-to-peer networks). A relationship of client and server may arise byvirtue of computer programs running on the respective computers andhaving a client-server relationship to each other.

While this specification contains many details, these should not beconstrued as limitations on the scope of what may be claimed, but ratheras descriptions of features specific to particular examples. Certainfeatures that are described in this specification in the context ofseparate implementations can also be combined. Conversely, variousfeatures that are described in the context of a single implementationcan also be implemented in multiple embodiments separately or in anysuitable sub-combination.

In a general aspect, this specification describes methods and systemsfor analyzing a well system fluid, such as, for example, a well cementslurry.

In some aspects, a method of analyzing a well cement slurry includesmixing a well cement slurry in a mixer (e.g., a laboratory mixer, afield mixer, etc.) under a plurality of conditions. The plurality ofconditions correspond to a plurality of distinct Reynolds number valuesfor the well cement slurry in the mixer. For example, each condition cancorrespond to a distinct value of one or more of the followingvariables: the rotational speed (N) of the impeller that agitates thewell cement slurry in the mixer, the density (ρ) of the well cementslurry, the apparent viscosity (μ) of the well cement slurry, andpossibly others. Power number values associated with mixing the wellcement slurry in the mixer under the plurality of conditions areidentified. Each power number value is based on measurements indicatingan amount of energy used to mix the well cement slurry under arespective one of the plurality of conditions. Values for parameters ofa functional relationship between power number (N_(p)) and Reynoldsnumber (Re) are identified based on the power number values and theReynolds number values for the plurality of conditions.

In some implementations, the functional relationship comprisesN_(p)=C(Re)^(x), and identifying values for the parameters of thefunctional relationship comprises identifying values for C and x. Insome cases, the functional relationship and the identified values forthe parameters can be used to compute a predicted power number valueassociated with mixing the well cement slurry under another distinctcondition. Here, the other distinct condition is different from theplurality of conditions that were used to compute the values of theparameters. For example, the other distinct condition can correspond toa different value of one or more of the following variables: therotational speed (N) of the impeller that agitates the well cementslurry in the mixer, the density (p) of the well cement slurry, theapparent viscosity (μ) of the well cement slurry, and possibly others.

In some cases, the functional relationship and the identified values forthe parameters can be used to compute a predicted power number valueassociated with mixing another well cement slurry, and the predictedpower number can be used to estimate the energy to mix the other wellcement slurry. In some cases, the functional relationship and theidentified values for the parameters can be used to determine amixability index associated with mixing the same or another well cementslurry. The mixability index can be a quantitative, objective index thatis related to the power number or another quantity.

A number of examples have been described. Various modifications can bemade without departing from the scope of the present disclosure.Accordingly, other embodiments are within the scope of the followingclaims.

What is claimed is:
 1. A method of analyzing a well cement slurry, themethod comprising: mixing a dry cement blend with mix water to form awell cement slurry in a mixer under a plurality of conditions, theplurality of conditions corresponding to a plurality of distinctReynolds number values for the well cement slurry in the mixer;identifying power number values associated with the mixing of the wellcement slurry in the mixer under the plurality of conditions, each powernumber value based on an amount of energy used to mix the well cementslurry under a respective one of the plurality of conditions; andidentifying values for parameters of a functional relationship betweenpower number and Reynolds number based on the power number values andthe Reynolds number values for the plurality of conditions, wherein: thepower number is dependent upon a time-varying fluid density measuredfrom when the dry cement blend is mixed with the mix water until thewell cement slurry is homogenous as confirmed by static or dynamic lightscattering, the Reynolds number is dependent upon a time-varyingapparent fluid viscosity measured from when the dry cement blend ismixed with the mix water until the well cement slurry is homogenous asconfirmed by static or dynamic light scattering, and the functionalrelationship with the identified values for the parameters is used todetermine a mixability index associated with the mixing to form anotherwell cement slurry.
 2. The method of claim 1, wherein the functionalrelationship comprises N_(p)=C(Re)^(x), and identifying values for theparameters of the functional relationship comprises identifying valuesfor C and x, where C and x are constants, N_(p) represents the powernumber, and Re represents the Reynolds number.
 3. The method of claim 1,wherein the mixer comprises an impeller that agitates the well cementslurry to mix the well cement slurry, and at least a subset of theplurality of conditions correspond to a plurality of distinct rotationalspeeds of the impeller.
 4. The method of claim 1, wherein at least asubset of the plurality of conditions correspond to a plurality ofdistinct densities of the well cement slurry.
 5. The method of claim 1,wherein at least a subset of the plurality of conditions correspond to aplurality of distinct viscosities of the well cement slurry.
 6. Themethod of claim 1, further comprising using the functional relationshipand the identified values for the parameters to compute a predictedpower number value associated with mixing the well cement slurry underanother distinct condition.
 7. The method of claim 6, further comprisingusing the predicted power number value to estimate the energy to mix thewell cement slurry under the other distinct condition.
 8. The method ofclaim 1, further comprising using the functional relationship with theidentified values for the parameters to compute a predicted power numbervalue associated with mixing the other well cement slurry.
 9. The methodof claim 8, further comprising using the predicted power number value toestimate the energy to mix the other well cement slurry.
 10. The methodof claim 9, further comprising: mixing the other well cement slurry; andafter mixing the other well cement slurry, communicating the other wellcement slurry in a wellbore in a subterranean region.